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    <title>glever</title>
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    <center>Scilab Function</center>
    <div align="right">Last update : 16/12/2004</div>
    <p>
      <b>glever</b> -  inverse of matrix pencil</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>[Bfs,Bis,chis]=glever(E,A [,s])  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>E, A</b>
        </tt>: two real square matrices of same dimensions</li>
      <li>
        <tt>
          <b>s</b>
        </tt>: character string (default value '<tt>
          <b>s</b>
        </tt>')</li>
      <li>
        <tt>
          <b>Bfs,Bis</b>
        </tt>: two polynomial matrices</li>
      <li>
        <tt>
          <b>chis</b>
        </tt>: polynomial</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
    Computation of</p>
    <p>
      <tt>
        <b>(s*E-A)^-1</b>
      </tt>
    </p>
    <p>
     by generalized Leverrier's algorithm for a matrix pencil.</p>
    <pre>

(s*E-A)^-1 = (Bfs/chis) - Bis.
   
    </pre>
    <p>
      <tt>
        <b>chis</b>
      </tt> = characteristic polynomial (up to a multiplicative constant).</p>
    <p>
      <tt>
        <b>Bfs</b>
      </tt>  = numerator polynomial matrix.</p>
    <p>
      <tt>
        <b>Bis</b>
      </tt>
    = polynomial matrix ( - expansion of <tt>
        <b>(s*E-A)^-1</b>
      </tt> at infinity).</p>
    <p>
    Note the - sign before <tt>
        <b>Bis</b>
      </tt>.</p>
    <h3>
      <font color="blue">Caution</font>
    </h3>
    <dl>
      <p>
    This function uses <tt>
          <b>cleanp</b>
        </tt> to simplify <tt>
          <b>Bfs,Bis</b>
        </tt> and <tt>
          <b>chis</b>
        </tt>.</p>
    </dl>
    <h3>
      <font color="blue">Examples</font>
    </h3>
    <pre>

s=%s;F=[-1,s,0,0;0,-1,0,0;0,0,s-2,0;0,0,0,s-1];
[Bfs,Bis,chis]=glever(F)
inv(F)-((Bfs/chis) - Bis)
 
  </pre>
    <h3>
      <font color="blue">See Also</font>
    </h3>
    <p>
      <a href="rowshuff.htm">
        <tt>
          <b>rowshuff</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="det.htm">
        <tt>
          <b>det</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="../polynomials/invr.htm">
        <tt>
          <b>invr</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="../polynomials/coffg.htm">
        <tt>
          <b>coffg</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="pencan.htm">
        <tt>
          <b>pencan</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="penlaur.htm">
        <tt>
          <b>penlaur</b>
        </tt>
      </a>,&nbsp;&nbsp;</p>
    <h3>
      <font color="blue">Author</font>
    </h3>
    <p>F. D. (1988)  </p>
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